COROLARY III.
The more the Cone is immerged, the more impossible is its floating.
And if we should more depress the Cone F T O, it would be so much the more impossible that it should sustain it self afloat, the part submerged N T O S still encreasing, and the Mass of Air contained in the Rampart diminishing, which ever grows less, the more the Cone submergeth.
That Cone, therefore, that with its Base upwards, and its Cuspis downwards doth swimme, being dimitted with its Base downward must of necessity sinke. They have argued farre from the truth, therefore, who have ascribed the cause of Natation to waters resistance of Division, as to a passive principle, and to the breadth of the Figure, with which the division is to be made, as the Efficient.
I come in the fourth place, to collect and conclude the reason of that which I have proposed to the Adversaries, namely,
THEOREME XII.
Solids of any Figure & greatnesse, that naturally sink, may by help of the Air in the Rampart swimme.
That it is possible [to fo{r}m Solid Bodies,] of what Figure and greatness soever, that of their own Nature goe to the Bottome; But by the help of the Air contained in the Rampart, rest without submerging.
The truth of this Proposition is sufficiently manifest in all those Solid Figures, that determine in their uppermost part in a plane Superficies: for making such Figures of some Matter specifically as grave as the water, putting them into the water, so that the whole Mass be covered, it is manifest, that they shall rest in all places, provided, that such a Matter equall in weight to the water, may be exactly adjusted: and they shall by consequence, rest or lie even with the Levell of the water, without making any Rampart. If, therefore, in respect of the Matter, such Figures are apt to rest without submerging, though deprived of the help of the Rampart, it is manifest, that they may admit so much encrease of Gravity, (without encreasing their Masses) as is the weight of as much water as would be contained within the Rampart, that is made about their upper plane Surface: by the help of which being sustained, they shall rest afloat, but being bathed, they shall descend, having been made graver than the water. In Figures, therefore, that determine above in a plane, we may cleerly comprehend, that the Rampart added or removed, may prohibit or permit the descent: but in those Figures that go lessening upwards towards the top, some Persons may, and that not without much seeming Reason, doubt whether the same may be done, and especially by those which terminate in a very acute Point, such as are your Cones and small Piramids. Touching these, therefore, as more dubious than the rest, I will endeavour to demonstrate, that they also lie under the same Accident of going, or not going to the Bottom, be they of any whatever bigness. Let therefore the Cone be A B D, made of a matter
specifically as grave as the water; it is manifest that being put all under water, it shall rest in all places (alwayes provided, that it shall weigh exactly as much as the water, which is almost impossible to effect) and that any small weight being added to it, it shall sink to the bottom: but if it shall descend downwards gently, I say, that it shall make the Rampart E S T O, and that there shall stay out of the water the point A S T, tripple in height to the Rampart E S: which is manifest, for the Matter of the Cone weighing equally with the water, the part submerged S B D T, becomes indifferent to move downwards or upwards; and the Cone A S T, being equall in Mass to the water that would be contained in the concave of the Rampart E S T O, shall be also equall unto it in Gravity: and, therefore, there shall be a perfect Equilibrium, and, consequently, a Rest. Now here ariseth a doubt, whether the Cone A B D may be made heavier, in such sort, that when it is put wholly under water, it goes to the bottom, but yet not in such sort, as to take from the Rampart the vertue of sustaining it that it sink not, and, the reason of the doubt is this: that although at such time as the Cone A B D is specifically as grave as the water, the Rampart E S T O sustaines it, not only when the point A S T is tripple in height to the Altitude of the Rampart E S, but also when a lesser part is above water; [for although in the Descent of the Cone the Point A S T by little and little
diminisheth, and so likewise the Rampart E S T O, yet the Point diminisheth in greater proportion than the Rampart, in that it diminisheth according to all the three Dimensions, but the Rampart according to two only, the Altitude still remaining the same; or, if you will, because the [Cone S {A} T] goes diminishing, according to the proportion of the cubes of the Lines that do successively become the Diameters of the Bases of emergent Cones, and the Ramparts diminish according to the proportion of the Squares of the same Lines; whereupon the proportions of the Points are alwayes Sesquialter of the proportions of the Cylinders, contained within the Rampart; so that if, for Example, the height of the emergent Point were double, or equall to the height of the Rampart, in these cases, the Cylinder contained within the Rampart, would be much greater than the said Point, because it would be either sesquialter or tripple, by reason of which it would perhaps serve over and above to sustain the whole Cone, since the part submerged would no longer weigh any thing;] yet, nevertheless, when any Gravity is added to the whole Mass of the Cone, so that also the part submerged is not without some excesse of Gravity above the Gravity of the water, it is not manifest, whether the Cylinder contained within the Rampart, in the descent that the Cone shall make, can be reduced to such a proportion unto the emergent Point, and to such an excesse of Mass above the Mass of it, as to compensate the excesse of the Cones Specificall Gravity above the Gravity of the water: and the Scruple ariseth, because that howbeit in the descent made by the Cone, the emergent Point A S T diminisheth, whereby there is also a diminution of the excess of the Cones Gravity above the Gravity of the water, yet the case stands so, that the Rampart doth also contract it self, and the Cylinder contained in it doth deminish. Nevertheless it shall be demonstrated, how that the Cone A B D being of any supposed bignesse, and made at the first of a Matter exactly equall in Gravity to the Water, if there may be affixed to it some Weight, by means [of which i{t} may descend] to the bottom, when submerged under water, it may also by vertue of the Rampart stay above without sinking.
Let, therefore, the Cone A B D be of any supposed greatnesse, and alike in specificall Gravity to the water. It is manifest, that being put lightly into the water, it shall rest without descending; and it
shall advance above water, the Point A S T, tripple in height to the height of the Rampart E S: Now, suppose the Cone A B D more depressed, so that it advance above water, only the Point A I R, higher by half than the Point A S T, with the Rampart about it C I R N. And, because, the Cone A B D is to the Cone A I R, as the cube of the Line S T is to the cube of the Line I R, but the Cylinder E S T O, is to the Cylinder C I R N, as the Square of S T to the Square of I R, the Cone A S T shall be Octuple to the Cone A I R, and the Cylinder E S T O, quadruple to the Cylinder C I R N: But the Cone A S T, is equall to the Cylinder E S T O: Therefore, the Cylinder C I R N, shall be double to the Cone A I R: and the water which might be contained in the Rampart C I R N, would be double in Mass and in Weight to the Cone A I R, and, therefore, would be able to sustain the double of the Weight of the Cone A I R: Therefore, if to the whole Cone A B D, there be added as much Weight as the Gravity of the Cone A I R, that is to say, the eighth part of the weight of the Cone A S T, it also shall be sustained by the Rampart C I R N, but without that it shall go to the bottome: the Cone A B D, being, by the addition of the eighth part of the weight of the Cone A S T, made specifically more grave than the water. But if the Altitude of the Cone A I R, were two thirds of the Altitude of the Cone A S T, the Cone A S T would be to the Cone A I R, as twenty seven to eight; and the Cylinder E S T O, to the Cylinder C I R N, as nine to four, that is, as twenty seven to twelve; and, therefore, the Cylinder C I R N, to the Cone A I R, as twelve to eight; and the excess of the Cylinder C I R N, above the Cone A I R, to the Cone A S T, as four to twenty seven: therefore if to the Cone A B D be added so much weight as is the four twenty sevenths of the weight of the Cone A S T, which is a little more then its seventh part, it also shall continue to swimme, and the height of the emergent Point shall be double to the height of the Rampart. This that hath been demonstrated in Cones, exactly holds in Piramides, although the one or the other should be very sharp in their Point or Cuspis: From whence we conclude, that the same Accident [Natatio{n} easiest effected] in Figures broad toward the top. shall so much the more easily happen in all other Figures, by how much the less sharp the Tops shall be, in which they determine, being assisted by more spacious Ramparts.
THEOREME XIII.
All Figures sink or swim, upon bathing or not bathing of their tops.
All Figures, therefore, of whatever greatnesse, may go, and not go, to the Bottom, according as their Sumities or Tops shall be bathed or not bathed.
And this Accident being common to all sorts of Figures, without exception of so much as one. Figure hath, therefore, no part in the production of this Effect, of sometimes sinking, and sometimes again not sinking, but only the being sometimes conjoyned to, and sometimes seperated from, the supereminent Air: which cause, in fine, who so shall rightly, and, as we say, with both his Eyes, consider this business, will find that it is reduced to, yea, that it really is the same with, the true, Naturall and primary cause of Natation or Submersion; to wit, the excess or deficiency of the Gravity of the water, in relation to the Gravity of that Solid Magnitude, that is demitted into the water. For like as a Plate of Lead, as thick as the back of a Knife, which being put into the water by it self alone goes to the bottom, if upon it you fasten a piece of Cork four fingers thick, doth continue afloat, for that now the Solid that is demitted in the water, is not, as before, more grave than the water, but less, so the Board of Ebony, of its own nature more grave than water; and, therefore, descending to the bottom, when it is demitted by it self alone into the water, if it shall be put upon the water, conjoyned with an Expanded vail of Air, that together with the Ebony doth descend, and that it be such, as that it doth make with it a compound less grave than so much water in Mass, as equalleth the Mass already submerged and depressed beneath the Levell of the waters Surface, it shall not descend any farther, but shall rest, for no other than the universall and most common cause, which is that Solid Magnitudes, less grave in specie than the water, go not to the bottom.
So that if one should take a Plate of Lead, as for Example, a finger thick, and an handfull broad every way, and should attempt to make it swimme, with putting it lightly on the water, he would lose his Labour, because that if it should be depressed an Hairs breadth beyond the possible Altitude of the Ramparts of water, it would dive and sink; but if whilst it is going downwards, one should make certain Banks or Ramparts about it, that should hinder the defusion of the water upon the said Plate, the which Banks should rise so high, as that they might be able to contain as much water, as should weigh equally with the said Plate, it would, [witho{u}t all Question,] descend no lower, but would rest, as being sustained by vertue of the Air contained within the aforesaid Ramparts: and, in short, there would be a Vessell by this means formed with the bottom of Lead. But if the thinness of the Lead shall be such, that a very small height of Rampart would suffice to contain so much Air, as might keep it afloat, it shall also rest without the Artificiall Banks or Ramparts, but yet not without the Air, because the Air by it self makes Banks sufficient for a small height, to resist the Superfusion of the water: so that that which in this case swimmes, is as it were a Vessell filled with Air, by vertue of which it continueth afloat.
I will, in the last place, [with an other Experime{n}t,] attempt to remove all difficulties, if so be there should yet be any doubt left in any one, touching the opperation of this *Continuity of the Air, [* Or rather Contiguity,] with the thin Plate which swims, and afterwards put an end to this part of my discourse.
I suppose my self to be questioning with some of my Oponents.
Whether Figure have any influence upon the encrease or diminution of the Resistance in any Weight against its being raised in the Air; and An Experiment of the operation of Figures, in encreasing or lessening of the Airs Resistance of Division. I suppose, that I am to maintain the Affirmative, asserting that a Mass of Lead, reduced to the Figure of a Ball, shall be raised with less force, then if the same had been made into a thinne and broad Plate, because that it in this spacious Figure, hath a great quantity of Air to penetrate, and in that other, more compacted and contracted very little: and to demonstrate the truth of such my Opinion, I will hang in a small thred first the Ball or Bullet, and put that into the water, tying the thred that upholds it to one end of the Ballance that I hold in the Air, and to the other end I by degrees adde so much Weight, till that at last it brings up the Ball of Lead out of the water: to do which, suppose a Gravity of thirty Ounces sufficeth; I afterwards reduce the said Lead into a flat and thinne Plate, the which I likewise put into the water, suspended by three threds, which hold it parallel to the Surface of the water, and putting in the same manner, Weights to the other end, till such time as the Plate comes to be raised and drawn out of the water: I finde that thirty six ounces will not suffice to seperate it from the water, and raise it thorow the Air: and arguing from this Experiment, I affirm, that I have fully demonstrated the truth of my Proposition. Here my Oponents desires me to look down, shewing me a thing which I had not before observed, to wit, that in the Ascent of the Plate out of the water, it draws after it another Plate (if I may so call it) of water, which before it divides and parts from the inferiour Surface of the Plate of Lead, is raised above the Levell of the other water, more than the thickness of the back of a Knife: Then he goeth to repeat the Experiment with the Ball, and makes me see, that it is but a very small quantity of water, which cleaves to its compacted and contracted Figure: and then he subjoynes, that its no wonder, if in seperating the thinne and broad Plate from the water, we meet with much greater Resistance, than in seperating the Ball, since together with the Plate, we are to raise a great quantity of water, which occurreth not in the Ball: He telleth me moreover, how that our Question is, whether the Resistance of Elevation be greater in a dilated Plate of Lead, than in a Ball, and not whether more resisteth a Plate of Lead with a great quantity of water, or a Ball with a very little water: He sheweth me in the close, that the putting the Plate and the Ball first into the water, to make proofe thereby of their Resistance in the Air, is besides our case, which treats of Elivating in the Air, and of things placed in the Air, and not of the Resistance that is made in the Confines of the Air and water, and by things which are part in Air and part in water: and lastly, they make me feel with my hand, that when the thinne Plate is in the Air, and free from the weight of the water, it is raised with the very same Force that raiseth the Ball. Seeing, and understanding these things, I know not what to do, unless to grant my self convinced, and to thank such a Friend, for having made me to see that which I never till then observed: and, being advertised by this same Accident, to tell my Adversaries, that our Question is, whether a Board and a Ball of Ebony, equally go to the bottom in water, and not a Ball of Ebony and a Board of Ebony, joyned with another flat Body of Air: and, farthermore, that we speak of sinking, and not sinking to the bottom, in water, and not of that which happeneth in the Confines of the water and Air to Bodies that be part in the Air, and part in the water; nor much less do we treat of the greater or lesser Force requisite in seperating this or that Body from the Air; not omitting to tell them, in the last place, that the Air doth resist, and gravitate downwards in the water, just so much as the water (if I may so speak) gravitates and resists upwards in the Air, and that the same Force is required to sinke a Bladder under water, that is full of Air, as to raise it in the Air, being full of water, removing the consideration of the weight of that Filme or Skinne, and considering the water and the Air only. And it is likewise true, that the same Force is required to sink a Cup or such like Vessell under water, whilst it is full of Air, as to raise it above the Superficies of the water, keeping it with the mouth downwards; whilst it is full of water, which is constrained in the same manner to follow the Cup which contains it, and to rise above the other water into the Region of the Air, as the Air is forced to follow the same Vessell under the Surface of the water, till [that in this c{a}se the water,] surmounting the brimme of the Cup, breaks in, driving thence the Air, and in that case, the said brimme coming out of the water, and arriving to the Confines of the Air, the water falls down, and the Air sub-enters to fill the cavity of the Cup: upon which ensues, that he no less transgresses the Articles of the Convention, who produceth a Plate conjoyned with much Air, to see if it descend to the bottom in water, then he that makes proof of the Resistance against Elevation in Air with a Plate of Lead, joyned with a like quantity of water.
Aristotles opinion touching the Operation of Figure examined.
I have said all that I could at present think of, to maintain the Assertion I have undertook. It remains, that I examine that which Aristotle hath writ of this matter towards the end of his Book De Cælo; wherein I shall note two things: the one that it being true as Aristot. de Cælo Lib. 4. Cap 6. hath been demonstrated, that Figure hath nothing to do about the moving or not moving it self upwards or downwards, its seemes that Aristotle at his first falling upon this Speculation, was of the same opinion, as in my opinion may be collected from the examination of his words. 'Tis true, indeed, that in essaying afterwards to render a reason of such effect, as not having in my conceit hit upon the right, (which in the second place I will examine) it seems that he is brought to admit the largenesse of Figure, to be interessed in this operation. As to the first particuler, hear the precise words of Aristotle.
Figures are not the Causes of moving simply upwards or downwards, but of moving more slowly or swiftly, and by what means this comes to Aristotle makes not Figure the cause of Motion absolutely, but of swift or slow motion, Lib. 4. Cap. 6: Text. 42. pass, it is not difficult to see.
Here first I note, that the terms being four, which fall under the present consideration, namely, Motion, Rest, Slowly and Swiftly: And Aristotle naming figures as Causes of Tardity and Velocity, excluding them from being the Cause of absolute and simple Motion, it seems necessary, that he exclude them on the other side, from being the Cause of Rest, so that his meaning is this. Figures are not the Causes of moving or not moving absolutely, but of moving quickly or slowly: and, here, if any should say the mind of Aristotle is to exclude Figures from being Causes of Motion, but yet not from being Causes of Rest, so that the sence would be to remove from Figures, there being the Causes of moving simply, but yet not there being Causes of Rest, I would demand, whether we ought with Aristotle to understand, that all Figures universally, are, in some manner, the causes of Rest in those Bodies, which otherwise would move, or else some particular Figures only, as for Example, broad and thinne Figures: If all indifferently, then every Body shall rest: because every Body hath some Figure, which is false; but if some particular Figures only may be in some manner a Cause of Rest, as, for Example, the broad, then the others would be in some manner the Causes of Motion: for if from seeing some Bodies of a contracted Figure move, which after dilated into Plates rest, may be inferred, that the Amplitude of Figure hath a part in the Cause of that Rest; so from seeing such like Figures rest, which afterwards contracted move, it may with the same reason be affirmed, that the united and contracted Figure, hath a part in causing Motion, as the remover of that which impeded it: The which again is directly opposite to what Aristotle saith, namely, that Figures are not the Causes of Motion. Besides, if Aristotle had admitted and not excluded Figures from being Causes of not moving in some Bodies, which moulded into another Figure would move, he would have impertinently propounded in a dubitative manner, in the words immediately following, whence it is, that the large and thinne Plates of Lead or Iron, rest upon the water, since the Cause was apparent, namely, the Amplitude of Figure. Let us conclude, therefore, that the meaning of Aristotle in this place is to affirm, that Figures are not the Causes of absolutely moving or not moving, but only of moving swiftly or slowly: which we ought the rather to believe, in regard it is indeed a most true conceipt and opinion. Now the mind of Aristotle being such, and appearing by consequence, rather contrary at the first sight, then favourable to the assertion of the Oponents, it is necessary, that their Interpretation be not exactly the same with that, but such, as being in part understood by some of them, and in part by others, was set down: and it may easily be indeed so, being an Interpretation consonent to the sence of the more famous Interpretors, which is, that the Adverbe Simply or Absolutely, put in the Text, ought not to be joyned to the Verbe to Move, but with the Noun Causes: so that the purport of Aristotles words, is to affirm, That Figures are not the Causes absolutely of moving or not moving, but yet are Causes Secundum quid, viz. in some sort; by which means, they are called Auxiliary and Concomitant Causes: and this Proposition is received and asserted as true by Signor Buonamico Lib. 5. Cap. 28. where he thus writes. There are other Causes concomitant, by which some things float, and others sink, among which the Figures of Bodies hath the first place, &c.
Concerning this Proposition, I meet with many doubts and difficulties, for which me thinks the words of Aristotle are not capable of such a construction and sence, and the difficulties are these.
First in the order and disposure of the words of Aristotle, the particle Simpliciter, or if you will absoluté, is conjoyned with the Verb to move, and seperated from the Noun Causes, the which is a great presumption in my favour, seeing that the writing and the Text saith, Figures are not the Cause of moving simply upwards or downwards, but of quicker or slower Motion: and, saith not, Figures are not simply the Causes of moving upwards or downwards, and when the words of a Text receive, transposed, a sence different from that which they sound, taken in the order wherein the Author disposeth them, it is not convenient to inverte them. And who will affirm that Aristotle desiring to write a Proposition, would dispose the words in such sort, that they should import a different, nay, a contrary sence? contrary, I say, because understood as they are written; they say, that Figures are not the Causes of Motion, but inverted, they say, that Figures are the Causes of Motion, &c.
Moreover, if the intent of Aristotle had been to say, that Figures are not simply the Causes of moving upwards or downwards, but only Causes Secundum quid, he would not have adjoyned those words, but they are Causes of the more swift or slow Motion; yea, the subjoining this would have been not only superfluous but false, for that the whole tenour of the Proposition would import thus much. Figures are not the absolute Causes of moving upwards or downwards, but are the absolute Cause of the swift or slow Motion; which is not true: because the primary Causes of greater or lesser Velocity, are by Aristotle in the 4th of his Physicks, Text. 71. attributed to the greater or lesser Gravity of Moveables, compared among themselves, and to the greater or lesser Resistance of the Medium's, depending on their greater or less Crassitude: and these are inserted by Aristotle as the primary Causes; and these two only are in that place nominated: and Figure comes afterwards to be considered, Text. 74. rather as an Instrumentall Cause of the force of the Gravity, the which divides either with the Figure, or with the Impetus; and, indeed, Figure by it self without the force of Gravity or Levity, would opperate nothing.
I adde, that if Aristotle had an opinion that Figure had been in some sort the Cause of moving or not moving, the inquisition which he makes immediately in a doubtfull manner, whence it comes, that a Plate of Lead flotes, would have been impertinent; for if but just before he had said, that Figure was in a certain sort the Cause of moving or not moving, he needed not to call in Question, by what Cause the Plate of Lead swims, and then ascribing the Cause to its Figure; and framing a discourse in this manner. Figure is a Cause Secundum quid of not sinking: but, now, if it be doubted, for what Cause a thin Plate of Lead goes not to the bottom; it shall be answered, that that proceeds from its Figure: a discourse which would be indecent in a Child, much more in Aristotle; For where is the occasion of doubting? And who sees not, that if Aristotle had held, that Figure was in some sort a Cause of Natation, he would without the least Hesitation have writ; That Figure is in a certain sort the Cause of Natation, and therefore the Plate of Lead in respect of its large and expatiated Figure swims; but if we take the proposition of Aristotle as I say, and as it is written, and as indeed it is true, the ensuing words come in very oppositely, as well in the introduction of swift and slow, as in the question, which very pertinently offers it self, and would say thus much.
Figures are not the Cause of moving or not moving simply upwards or downwards, but of moving more quickly or slowly: But if it be so, the Cause is doubtfull, whence it proceeds, that a Plate of Lead or of Iron broad and thin doth swim, &c. And the occasion of the doubt is obvious, because it seems at the first glance, that the Figure is the Cause of this Natation, since the same Lead, or a less quantity, but in another Figure, goes to the bottom, and we have already affirmed, that the Figure hath no share in this effect.
Lastly, if the intent of Aristotle in this place had been to say, that Figures, although not absolutely, are at least in some measure the Cause of moving or not moving: I would have it considered, that he names no less the Motion upwards, than the other downwards: and because in exemplifying it afterwards, he produceth no other Experiments than of a Plate of Lead, and Board of Ebony, Matters that of their own Nature go to the bottom, but by vertue (as our Adversaries say) of their Figure, rest afloat; it is fit that they should produce some other Experiment of those Matters, which by their Nature swims, but retained by their Figure rest at the bottom. But since this is impossible to be done, we conclude, that Aristotle in this place, hath not attributed any action to the Figure of simply moving or not moving.
But though he hath exquisitely Philosophiz'd, in investigating the solution of the doubts he proposeth, yet will I not undertake to maintain, rather various difficulties, that present themselves unto me, give me occasion of suspecting that he hath not entirely displaid unto us, the true Cause of the present Conclusion: which difficulties I will propound one by one, ready to change opinion, whenever I am shewed, that the Truth is different from what I say; to the confession whereof I am much more inclinable than to contradiction.
Aristotle erred in affirming a Needle dimitted long wayes to sink.
Aristotle having propounded the Question, whence it proceeds, that broad Plates of Iron or Lead, float or swim; he addeth (as it were strengthening the occasion of doubting) forasmuch as other things, less, and less grave, be they round or long, as for instance a Needle go to the bottom. Now I here doubt, or rather am certain that a Needle put lightly upon the water, rests afloat, no less than the thin Plates of Iron or Lead. I cannot believe, albeit it hath been told me, that some to defend Aristotle should say, that he intends a Needle demitted not longwayes but endwayes, and with the Point downwards; nevertheless, not to leave them so much as this, though very weak refuge, and which in my judgement Aristotle himself would refuse, I say it ought to be understood, that the Needle must be demitted, according to the Dimension named by Aristotle, which is the length: because, if any other Dimension than that which is named, might or ought to be taken, I would say, that even the Plates of Iron and Lead, sink to the bottom, if they be put into the water edgewayes and not flatwayes. But because Aristotle saith, broad Figures go not to the bottom, it is to be understood, being demitted broadwayes: and, therefore, when he saith, long Figures as a Needle, albeit light, rest not afloat, it ought to be understood of them when demitted longwayes.
Moreover, to say that Aristotle is to be understood of the Needle demitted with the Point downwards, is to father upon him a great impertinency; for in this place he saith, that little Particles of Lead or Iron, if they be round or long as a Needle, do sink to the bottome; so that by his Opinion, a Particle or small Grain of Iron cannot swim: and if he thus believed, what a great folly would it be to subjoyn, that neither would a Needle demitted endwayes swim? And what other is such a Needle, but many such like Graines accumulated one upon another? It was too unworthy of such a man to say, that one single Grain of Iron could not swim, and that neither can it swim, though you put a hundred more upon it.
Lastly, either Aristotle believed, that a Needle demitted longwayes upon the water, would swim, or he believed that it would not swim: If he believed it would not swim, he might well speak as indeed he did; but if he believed and knew that it would float, why, together with the dubious Problem of the Natation of broad Figures, though of ponderous Matter, hath he not also introduced the Question; whence it proceeds, that even long and slender Figures, howbeit of Iron or Lead do swim? And the rather, for that the occasion of doubting seems greater in long and narrow Figures, than in broad and thin, as from Aristotles not having doubted of it, is manifested.
No lesser an inconvenience would they fasten upon Aristotle, who in his defence should say, that he means a Needle pretty thick, and not a small one; for take it for granted to be intended of a small one; and it shall suffice to reply, that he believed that it would swim; and I will again charge him with having avoided a more wonderfull and intricate Probleme, and introduced the more facile and less wonderfull.
We say freely therefore, that Aristotle did hold, that only the broad Figure did swim, but the long and slender, such as a Needle, not. The which nevertheless is false, as it is also false in round Bodies: because, as from what hath been predemonstrated, may be gathered, little Balls of Lead and Iron, do in like manner swim.
Aristotle affirmeth some Bodies volatile for their Minuity, Text. 42.
He proposeth likewise another Conclusion, which likewise seems different from the truth, and it is, That some things, by reason of their littleness fly in the Air, as the small dust of the Earth, and the thin leaves of beaten Gold: but in my Opinion, Experience shews us, that that happens not only in the Air, but also in the water, in which do descend, even those Particles or Atomes of Earth, that disturbe it, whose minuity is such, that they are not deservable, save only when they are many hundreds together. Therefore, the dust of the Earth, and beaten Gold, do not any way sustain themselves in the Air, but descend downwards, and only fly to and again in the same, when strong Windes raise them, or other agitations of the Air commove them: and this also happens in the commotion of the water, which raiseth its Sand from the bottom, and makes it muddy. But Aristotle cannot mean this impediment of the commotion, of which he makes no mention, nor names other than the lightness of such Minutiæ or Atomes, and the Resistance of the Crassitudes of the Water and Air, by which we see, that he speakes of a calme, and not disturbed and agitated Air: but in that case, neither Gold nor Earth, be they never so small, are sustained, but speedily descend.
Democritus placed the Cause of Natation in certain fiery Atomes.
He passeth next to confute Democritus, which, by his Testimony would Aristot. De Cælo lib. 4. cap. 6. text. 43. have it, that some Fiery Atomes, which continually ascend through the water, do spring upwards, and sustain those grave Bodies, which are very broad, and that the narrow descend to the bottom, for that but a small quantity of those Atomes, encounter and resist them.
Democritus confuted by Aristotle, text 43.
I say, Aristotle confutes this position, saying, that that should much more occurre in the Air, as the same Democritus instances against himself, but after he had moved the objection, he slightly resolves it, with saying, that those Corpuscles which ascend in the Air, make not their Impetus conjunctly. Here I will not say, that the reason alledged by Democritus is true, but I will only say, it Aristotles confutation of Democritus refuted by the Author. seems in my judgement, that it is not wholly confuted by Aristotle, whilst he saith, that were it true, that the calid ascending Atomes, should sustain Bodies grave, but very broad, it would much more be done in the Air, than in Water, for that haply in the Opinion of Aristotle, the said calid Atomes ascend with much greater Force and Velocity through the Air, than through the water. And if this be so, as I verily believe it is, the Objection of Aristotle in my judgement seems to give occasion of suspecting, that he may possibly be deceived in more than one particular: First, because those calid Atomes, (whether they be Fiery Corpuscles, or whether they be Exhalations, or in short, whatever other matter they be, that ascends upwards through the Air) cannot be believed to mount faster through Air, than through water: but rather on the contrary, they peradventure move more impetuously through the water, than through the Air, as hath been in part demonstrated above. And here I cannot finde the reason, why Aristotle seeing, that the descending Motion of the same Moveable, is more swift in Air, than in water, hath not advertised us, that from the contrary Motion, the contrary should necessarily follow; to wit, that it is more swift in the water, than in the Air: for since that the Moveable which descendeth, moves swifter through the Air, than through the water, if we should suppose its Gravity gradually to diminish, it would first become such, that descending swiftly through the Air, it would descend but slowly through the water: and then again, it might be such, that descending in the Air, it should ascend in the water: and being made yet less grave, it shall ascend swiftly through the water, and yet descend likewise through the Air: and in short, before it can begin to ascend, though but slowly through the Air, it shall ascend swiftly through the water: how then is it true, that ascending Moveables move swifter through the Air, than through the water?
That which hath made Aristotle believe, the Motion of Ascent to be swifter in Air, than in water, was first, the having referred the Causes of slow and quick, as well in the Motion of Ascent, as of Descent, only to the diversity of the Figures of the Moveable, and to the more or less Resistance of the greater or lesser Crassitude, or Rarity of the Medium; not regarding the comparison of the Excesses of the Gravities of the Moveables, and of the Mediums: the which notwithstanding, is the most principal point in this affair: for if the augmentation and diminution of the Tardity or Velocity, should have only respect to the Density or Rarity of the Medium, every Body that descends in Air, would descend in water: because whatever difference is found between the Crassitude of the water, and that of the Air, may well be found between the Velocity of the same Moveable in the Air, and some other Velocity: and this should be its proper Velocity in the water, which is absolutely false. The other occasion is, that he did believe, that like as there is a positive and intrinsecall Quality, whereby Elementary Bodies have a propension of moving towards the Centre of the Earth, so there is another likewise intrinsecall, whereby some of those Bodies have an Impetus of flying Lib. 4. Cap. 5. the Centre, and moving upwards: by Vertue of which intrinsecall Principle, called by him Levity, the Moveables which have that same Motion more easily penetrate the more subtle Medium, than the more dense: but such a Proposition appears likewise uncertain, as I have above hinted in part, and as with Reasons and Experiments, I could demonstrate, did not the present Argument importune me, or could I dispatch it in few words.
The Objection therefore of Aristotle against Democritus, whilst he saith, that if the Fiery ascending Atomes should sustain Bodies grave, but of a distended Figure, it would be more observable in the Air than in the water, because such Corpuscles move swifter in that, than in this, is not good; yea the contrary would evene, for that they ascend more slowly through the Air: and, besides their moving slowly, they ascend, not united together, as in the water, but discontinue, and, as we say, scatter: And, therefore, as Democritus well replyes, resolving the instance they make not their push or Impetus conjunctly.
Aristotle, in the second place, deceives himself, whilst he will have the said grave Bodies to be more easily sustained by the said Fiery ascending Atomes in the Air than in the Water: not observing, that the said Bodies are much more grave in that, than in this, and that such a Body weighs ten pounds in the Air, which will not in the water weigh 1/2 an ounce; how can it then be more easily sustained in the Air, than in the Water?
Democritus confuted by the Authour.
Let us conclude, therefore, that Democritus hath in this particular better Philosophated than Aristotle. But yet will not I affirm, that Democritus hath reason'd rightly, but I rather say, that there is a manifest Experiment that overthrows his Reason, and this it is, That if it were true, that calid ascending Atomes should uphold a Body, that if they did not hinder, would go to the bottom, it would follow, that we may find a Matter very little superiour in Gravity to the water, the which being reduced into a Ball, or other contracted Figure, should go to the bottom, as encountring but few Fiery Atomes; and which being distended afterwards into a dilated and thin Plate, should come to be thrust upwards by the impulsion of a great Multitude of those Corpuscles, and at last carried to the very Surface of the water: which wee see not to happen; Experience shewing us, that a Body v. gra. of a Sphericall Figure, which very hardly, and with very great leasure goeth to the bottom, will rest there, and will also descend thither, being reduced into whatsoever other distended Figure. We must needs say then, either that in the water, there are no such ascending Fiery Atoms, or if that such there be, that they are not able to raise and lift up any Plate of a Matter, that without them would go to the bottom: Of which two Positions, I esteem the second to be true, understanding it of water, constituted in its naturall Coldness. But if we take a Vessel of Glass, or Brass, or any other hard matter, full of cold water, within which is put a Solid of a flat or concave Figure, but that in Gravity exceeds the water so little, that it goes slowly to the bottom; I say, that putting some burning Coals under the said Vessel, as soon as the new Fiery Atomes shall have penetrated the substance of the Vessel, they shall without doubt, ascend through that of the water, and thrusting against the foresaid Solid, they shall drive it to the Superficies, and there detain it, as long as the incursions of the said Corpuscles shall last, which ceasing after the removall of the Fire, the Solid being abandoned by its supporters, shall return to the bottom.
But Democritus notes, that this Cause only takes place when we treat of raising and sustaining of Plates of Matters, but very little heavier than the water, or extreamly thin: but in Matters very grave, and of some thickness, as Plates of Lead or other Mettal, that same Effect wholly ceaseth: In Testimony of which, let's observe that such Plates, being raised by the Fiery Atomes, ascend through all the depth of the water, and stop at the Confines of the Air, still staying under water: but the Plates of the Opponents stay not, but only when they have their upper Superficies dry, nor is there any means to be used, that when they are within the water, they may not sink to the bottom. The cause, therefore, of the Supernatation of the things of which Democritus speaks is one, and that of the Supernatation of the things of which we speak is another. But, returning to Aristotle, Aristotle shews his desire of finding Democritus in an Error, to exceed that of discovering Truth. methinks that he hath more weakly confuted Democritus, than Democritus himself hath done: For Aristotle having propounded the Objection which he maketh against him, and opposed him with saying, that if the calid ascendent Corpuscles were those that raised the thin Plate, much more then would such a Solid be raised and born upwards through the Air, it sheweth that the desire in Aristotle to detect Democritus, was predominate over the exquisiteness of Solid Philosophizing: which desire of his he hath discovered in other occasions, and that we may not digress too far from this place, in the Text precedent to this Chapter which we have in hand; where he Cap. 5. Text 41. attempts to confute the same Democritus for that he, not contenting himself with names only, had essayed more particularly to declare what things Gravity and Levity were; that is, the Causes of descending and ascending, (and had introduced Repletion and Vacuity) ascribing this to Fire, by which it moves upwards, and that to the Earth, by which it descends; afterwards attributing to the Air more of Fire, and to the water more of Earth. But Aristotle desiring a positive Cause, even of ascending Motion, and not as Plato, or these others, a simple negation, or privation, such as Vacuity would be in reference to Repletion, argueth against Democritus and saith: If it be true, as Id. ibid. you suppose, then there shall be a great Mass of water, which shall have more of Fire, than a small Mass of Air, and a great Mass of Air, which shall have more of Earth than a little Mass of water, whereby it would ensue, that a great Mass of Air, should come more swiftly downwards, than a little quantity of water: But that is never in any case soever: Therefore Democritus discourseth erroneously.
But in my opinion, the Doctrine of Democritus is not by this allegation overthrown, but if I erre not, the manner of Aristotle deduction either concludes not, or if it do conclude any thing, it may with equall force be restored against himself. Democritus will grant to Aristotle, that there may be a great Mass of Air taken, which contains more Earth, than a small quantity of water, but yet will deny, that such a Mass of Air, shall go faster downwards than a little water, and that for many reasons. First, because if the greater quantity of Earth, contained in the great Mass of Air, ought to cause a greater Velocity than a less quantity of Earth, contained in a little quantity of water, it would be necessary, first, that it were true, that a greater Mass of pure Earth, should move more swiftly than a less: But this is false, though Aristotle in many places affirms it to be true: because not the greater absolute, but the greater specificall Gravity, is the cause of greater Velocity: nor doth a Ball The greater Specificall, not the greater absolute Gravity, is the Cause of Velocity. of Wood, weighing ten pounds, descend more swiftly than one weighing ten Ounces, and that is of the same Matter: but indeed a Bullet of Lead of four Ounces, descendeth more swiftly than a Ball of Wood of twenty Pounds: because the Lead is more grave in specie than the Wood. Therefore, its not necessary, that a great Mass of Air, by reason of the much Earth contained in it, do descend more swiftly than a little Mass of water, but on the contrary, any whatsoever Mass of Any Mass of water shal move more swiftly, than any of Air, and why. water, shall move more swiftly than any other of Air, by reason the participation of the terrene parts in specie is greater in the water, than in the Air. Let us note, in the second place, how that in multiplying the Mass of the Air, we not only multiply that which is therein of terrene, but its Fire also: whence the Cause of ascending, no less encreaseth, by vertue of the Fire, than that of descending on the account of its multiplied Earth. It was requisite in increasing the greatness of the Air, to multiply that which it hath of terrene only, leaving its Fire in its first state, for then the terrene parts of the augmented Air, overcoming the terrene parts of the small quantity of water, it might with more probability have been pretended, that the great quantity of Air, ought to descend with a greater Impetus, than the little quantity of water.
Therefore, the Fallacy lyes more in the Discourse of Aristotle, than in that of Democritus, who with severall other Reasons might oppose Aristotle, and alledge; If it be true, that the extreame Elements be one simply grave, and the other simply light, and that the mean Elements participate of the one, and of the other Nature; but the Air more of Levity, and the water more of Gravity, then there shall be a great Mass of Air, whose Gravity shall exceed the Gravity of a little quantity of water, and therefore such a Mass of Air shall descend more swiftly than that little water: But that is never seen to occurr: Therefore its not true, that the mean Elements do participate of the one, and the other quality. This argument is fallacious, no less than the other against Democritus.
Lastly, Aristotle having said, that if the Position of Democritus were true, it would follow, that a great Mass of Air should move more swiftly than a small Mass of water, and afterwards subjoyned, that that is never seen in any Case: methinks others may become desirous to know of him in what place this should evene, which he deduceth against Democritus, and what Experiment teacheth us, that it never falls out so. To suppose to see it in the Element of water, or in that of the Air is vain, because neither doth water through water, nor Air through Air move, nor would they ever by any whatever participation others assign them, of Earth or of Fire: the Earth, in that it is not a Body fluid, and yielding to the mobility of other Bodies, is a most improper place and Medium for such an Experiment: Vacuum, according to the same Aristotle himself, there is none, and were there, nothing would move in it: there remains the Region of Fire, but being so far distant from us, what Experiment can assure us, or hath assertained Aristotle in such sort, that he should as of a thing most obvious to sence, affirm what he produceth in confutation of Democritus, to wit, that a great Mass of Air, is moved no swifter than a little one of water? But I will dwell no longer upon this matter, whereon I have spoke sufficiently: but leaving Democritus, I return to the Text of Aristotle, wherein he goes about to render the true reason, how it comes to pass, that the thin Plates of Iron or Lead do swim on the water; and, moreover, that Gold it self being beaten into thin Leaves, not only swims in water, but flyeth too and again in the Air. He supposeth that of Continualls, some are easily De Cælo l. 4. c. 6. t. 44. divisible, others not: and that of the easily divisible, some are more so, and some less: and these he affirms we should esteem the Causes. He addes that that is easily divisible, which is well terminated, and the more the more divisible, and that the Air is more so, than the water, and the water than the Earth. And, lastly, supposeth that in each kind, the lesse quantity is easlyer divided and broken than the greater.
Here I note, that the Conclusions of Aristotle in generall are all true, but methinks, that he applyeth them to particulars, in which they have no place, as indeed they have in others, as for Example, Wax is more easily divisible than Lead, and Lead than Silver, inasmuch as Wax receives all the terms more easlier than Lead, and Lead than Silver. Its true, moreover, that a little quantity of Silver is easlier divided than a great Mass: and all these Propositions are true, because true it is, that in Silver, Lead and Wax, there is simply a Resistance against Division, and where there is the absolute, there is also the respective. But if as well in water as in Air, there be no Renitence against simple Division, how can we say, that the water is easlier divided than the Air? We know not how to extricate our selves from the Equivocation: whereupon I return to answer, that Resistance of absolute Division is one thing, and Resistance of Division made with such and such Velocity is another. But to produce Rest, and to abate the Motion, the Resistance of absolute Division is necessary; and the Resistance of speedy Division, causeth not Rest, but slowness of Motion. But that as well in the Air, as in water, there is no Resistance of simple Division, is manifest, for that there is not found any Solid Body which divides not the Air, and also the water: and that beaten Gold, or small dust, are not able to superate the Resistance of the Air, is contrary to that which Experience shews us, for we see Gold and Dust to go waving to and again in the Air, and at last to descend downwards, and to do the same in the water, if it be put therein, and separated from the Air. And, because, as I say, neither the water, nor the Air do resist simple Division, it cannot be said, that the water resists more than the Air. Nor let any object unto me, the Example of most light Bodies, as a Feather, or a little of the pith of Elder, or water-reed that divides the Air and not the water, and from this infer, that the Air is easlier divisible than the water; for I say unto them, that if they do well observe, they shall see the same Body likewise divide the Continuity of the water, and Archimed. De Insident. humi lib. 2. prop. 1. submerge in part, and in such a part, as that so much water in Mass would weigh as much as the whole Solid. And if they shal yet persist in their doubt, that such a Solid sinks not through inability to divide the water, I will return them this reply, that if they put it under water, and then let it go, they shall see it divide the water, and presently ascend with no less celerity, than that with which it divided the Air in descending: so that to say that this Solid ascends in the Air, but that coming to the water, it ceaseth its Motion, and therefore the water is more difficult to be divided, concludes nothing: for I, on the contrary, will propose them a piece of Wood, or of Wax, which riseth from the bottom of the water, and easily divides its Resistance, which afterwards being arrived at the Air, stayeth there, and hardly toucheth it; whence I may aswell say, that the water is more easier divided than the Air.
I will not on this occasion forbear to give warning of another fallacy of these persons, who attribute the reason of sinking or swimming to the greater or lesse Resistance of the Crassitude of the water against Division, making use of the example of an Egg, which in sweet water goeth to the bottom, but in salt water swims; and alledging for the cause thereof, the faint Resistance of fresh water against Division, and the strong Resistance of salt water. But if I mistake not, from the same Experiment, we may aswell deduce the quite contrary; namely, that the fresh water is more dense, and the salt more tenuous and subtle, since an Egg from the bottom of salt water speedily ascends to the top, and divides its Resistance, which it cannot do in the fresh, in whose bottom it stays, being unable to rise upwards. Into such like perplexities, do false Principles Lead men: but he that rightly Philosophating, shall acknowledge the excesses of the Gravities of the Moveables and of the Mediums, to be the Causes of those effects, will say, that the Egg sinks to the bottom in fresh water, for that it is more grave than it, and swimeth in the salt, for that its less grave than it: and shall without any absurdity, very solidly establish his Conclusions.
Therefore the reason totally ceaseth, that Aristotle subjoyns in the Text saying; The things, therefore, which have great breadth remain Text 45. above, because they comprehend much, and that which is greater, is not easily divided. Such discoursing ceaseth, I say, because its not true, that there is in water or in Air any Resistance of Division; besides that the Plate of Lead when it stays, hath already divided and penetrated the Crassitude of the water, and profounded it self ten or twelve times more than its own thickness: besides that such Resistance of Division, were it supposed to be in the water, could not rationally be affirmed to be more in its superiour parts than in the middle, and lower: but if there were any difference, the inferiour should be the more dense, so that the Plate would be no less unable to penetrate the lower, than the superiour parts of the water; nevertheless we see that no sooner do we wet the superiour Superficies of the Board or thin Piece of Wood, but it precipitatly, and without any retension, descends to the bottom.
I believe not after all this, that any (thinking perhaps thereby to defend Aristotle) will say, that it being true, that the much water resists more than the little, the said Board being put lower descendeth, because there remaineth a less Mass of water to be divided by it: because if after the having seen the same Board swim in four Inches of water, and also after that in the same to sink, he shall try the same Experiment upon a profundity of ten or twenty fathom water, he shall see the very self same effect. And here I will take occasion to remember, for the removall of an Error that is too common; That that Ship or other whatsoever Body, that on the depth of an hundred or a thousand fathom, swims with submerging only six fathom of its own height, [or in the Sea dialect, that draws six fathom water] shall swim in the same manner in water, that hath but six fathom and half an Inch of depth. Nor do I on the other side, think that it can be said, A Ship that in 100 Fathome water draweth 6 Fathome, shall float in 6 Fathome and 1/2 an Inch of depth. that the superiour parts of the water are the more dense, although a most grave Authour hath esteemed the superiour water in the Sea to be so, grounding his opinion upon its being more salt, than that at the bottom: but I doubt the Experiment, whether hitherto in taking the water from the bottom, the Observatour did not light upon some spring of fresh water there spouting up: but we plainly see on the contrary, the fresh Waters of Rivers to dilate themselves for some miles beyond their place of meeting with the salt water of the Sea, without descending in it, or mixing with it, unless by the intervention of some commotion or turbulency of the Windes.
But returning to Aristotle, I say, that the breadth of Figure hath nothing to do in this business more or less, because the said Plate of Lead, or other Matter, cut into long Slices, swim neither more nor less; and the same shall the Slices do, being cut anew into little Thickness not breadth of Figure to be respected in Natation. pieces, because its not the breadth but the thickness that operates in this business. I say farther, that in case it were really true, that the Renitence to Division were the proper Cause of swimming, the Were Renitence the cause of Natation, breadth of Figure would hinder the swiming of Bodies. Figures more narrow and short, would much better swim than the more spacious and broad, so that augmenting the breadth of the Figure, the facility of supernatation will be deminished, and decreasing, that this will encrease.
And for declaration of what I say, consider that when a thin Plate of Lead descends, dividing the water, the Division and discontinuation is made between the parts of the water, invironing the perimeter or Circumference of the said Plate, and according to the bigness greater or lesser of that circuit, it hath to divide a greater or lesser quantity of water, so that if the circuit, suppose of a Board, be ten Feet in sinking it flatways, it is to make the seperation and division, and to so speak, an incission upon ten Feet of water; and likewise a lesser Board that is four Feet in Perimeter, must make an incession of four Feet. This granted, he that hath any knowledge in Geometry, will comprehend, not only that a Board sawed in many long thin pieces, will much better float than when it was entire, but that all Figures, the more short and narrow they be, shall so much the better swim. Let the Board A B C D be, for Example, eight Palmes long, and five broad, its circuit shall be twenty six Palmes; and so many must the incession be, which it shall make in the water to descend therein: [but if we do saw ir,] as suppose into eight little pieces, according to the Lines E F, G H, [{&}c. making seven Segments,] we must adde to the twenty six Palmes of the circuit of the whole Board, seventy others; whereupon the eight little pieces so cut and seperated, have to cut ninty six Palmes of water. And, if moreover, we
cut each of the said pieces into five parts, reducing them into Squares, to the circuit of ninty six Palmes, with four cuts of eight Palmes apiece; we shall adde also sixty four Palmes, whereupon the said Squares to descend in the water, must divide one hundred and sixty Palmes of water, but the Resistance is much greater than that of twenty six; therefore to the lesser Superficies, we shall reduce them, so much the more easily will they float: and the same will happen in all other Figures, whose Superficies are simular amongst themselves, but different in bigness: because the said Superficies, being either deminished or encreased, always diminish or encrease their Perimeters in subduple proportion; to wit, the Resistance that they find in penetrating the water; therefore the little pieces gradually swim, with more and more facility as their breadth is lessened.
This is manifest; for keeping still the same height of the Solid, with the same proportion as the Base encreaseth or deminisheth, doth the said Solid also encrease or diminish; whereupon the Solid more diminishing than the Circuit, the Cause of Submersion more diminisheth than the Cause of Natation: And on the contrary, the Solid more encreasing than the Circuit, the Cause of Submersion encreaseth more, that of Natation less.
And this may all be deduced out of the Doctrine of Aristotle against his own Doctrine.
Lib. 4. c. 6. Text 45.
Lastly, to that which we read in the latter part of the Text, that is to say, that we must compare the Gravity of the Moveable with the Resistance of the Medium against Division, because if the force of the Gravity exceed the Resistance of the Medium, the Moveable will descend, if not it will float. I need not make any other answer, but that which hath been already delivered; namely, that its not the Resistance of absolute Division, (which neither is in Water nor Air) but the Gravity of the Medium that must be compared with the Gravity of the Moveables; and if that of the Medium be greater, the Moveable shall not descend, nor so much as make a totall Submersion, but a partiall only; because in the place which it would occupy in the water, there must not remain a Body that weighs less than a like quantity of water: but if the Moveable be more grave, it shall descend to the bottom, and possess a place where it is more conformable for it to remain, than another Body that is less grave. And this is the only true proper and absolute Cause of Natation and Submersion, so that nothing else hath part therein: and the Board of the Adversaries swimmeth, when it is conjoyned with as much Air, as, together with it, doth form a Body less grave than so much water as would fill the place that the said Compound occupyes in the water; but when they shall demit the simple Ebony into the water, according to the Tenour of our Question, it shall alwayes go to the bottom, though it were as thin as a Paper.
FINIS.
Detailed Transcriber's Notes
The text has been made to match the original text as much as possible including variation in spelling, punctuation, italics etc. The following, details apparent printer's errors as well as changes or additions to aid readability of text.
Page [1], missing full stop after abbreviation gr., ['0 gr 54 min.'].
Page [3], sidenote, missing space between words, ['the Authority ofan Author.'].
Page [3], printer's error, augmentarion for augmentation, ['and augmentarion of Masse'].
Page [4], missing letter t, ['tha{t} that proceeded not'].
Page [4], printer's error or inconsistent punctuation, ['my paynes and time. and although'].
Page [6], inconsistent punctuation, full stop after axiome where as there are none after those following, ['AXIOME. I.'].
Page [9], missing full stop added to end of paragraph, ['or else an upright Prisme.'].
Page [11], printer's error, missing letter C in illustration, ['the Prisme A C D B to be placed'].
Page [15], printer's error or archaic lettering, final y looking like a 7 in original text, ['and of the Specifick Gravit{y}'].
Page [16], letter N for T in text to refer to illustration, [if the Vessell E N S F'].
Page [16], printer's error, duplicate word in text, ['equalizeth the Force and and Moment,'].
Page [17], printer's error, rhe for the, ['as in rhe Stilliard,'].
Page [17], missing space between words, ['asoften as that'].
Page [18], printer's error, specifiaclly for specifically, ['A Solid specifiaclly graver'].
Page [20], potential printer's error, properly for property, ['but this properly they have'].
Page [20], printer's error, n for u, ['loseth all a{u}thenticalness'].
Page [22], printer's error or variation in spelling, Benonamico for Buonamico, ['it seemes that Benonamico'].
Page [23], printer's error, missing i, ['accordng to its excess'].
Page [24], missing line at the end of page in original text, ['its Region it loseth all'].
Page [26], missing letter n, ['u{n}able by its small weight'].
Page [29], missing letter e, ['that I have gon{e} about'].
Page [32], unclear symbol in original text, ['other Figure, {&}c.'].
Page [37], potential printer's error, comma in unusual position, ['whatever Figure, goeth always'].
Page [38], missing space between words, ['Superficies might bedry:'].
Page [39], missing letter t, unied for united, ['which holds them unied,'].
Page [41], printer's error, Motitions for Motions, ['all Motitions are made'].
Page [42], sidenote, possible missing letter e, ['Se{e} what satisfaction'].
Page [43], printer's error, Subdidivisions for Subdivisions, ['other Subdidivisions,'].
Page [49], missing letter i, dminishing for diminishing, ['or dminishing it by dividing'].
Page [50], sidenote, printer's error, missing letter l, hep for help, ['float by hep of'].
Page [53], printer's error, missing letter n, beig for being, ['beig double in Gravity'].
Page [54], printer's error, missing letter l, ['sha{l}l also descend.'].
Page [55], printer's error, missing letter r, ['to fo{r}m Solid Bodies,'].
Page [56], printer's error, missing letter A, ['Cone S {A} T'].
Page [57], printer's error, missing letter t, ['of which i{t} may descend'].
Page [58], sidenote, printer's error, inverted n, ['Natatio{n} easiest effected'].
Page [59], missing letter u, ['witho{u}t all Question,'].
Page [59], printer's error, inverted n, ['with an other Experime{n}t'].
Page [59], potential printer's error, sidenote ends with comma, ['Or rather Contiguity,'].
Page [61], missing letter a, ['that in this c{a}se the water,'].
Page [74], printer's error, ir for it, ['but if we do saw ir,'].
Page [75], unclear symbol in original text, ['{&}c. making seven Segments'].